Does blender offer a posterization option for rendering?
Not as such, no. But there is a toon shader for Blender Internal, and some similar results have been developed for Cycles.

What is probably more useful to you is a compositing setup that will operate on the render, rather than the material. Some success has been had with this node setup, using the "Round" algorithm. It separates RGB, rounds each to the nearest 0.1, and then recombines them.

Hope that helps!